Polonius sends his servant Reynaldo to Paris to give Laertes some money and letters, but also to secretly check up on him. Polonius's instructions are so detailed and complicated that they are absurd.
Polonius is established here as a meddler; he instructs Reynaldo in using appearance to hide reality.
Ophelia enters, upset. She tells Polonius that Hamlet burst into her room and held her wrists, studying her face and sighing. Then he left without a word.
Is Hamlet pretending, or is he actually mad? The answer isn't clear.
Polonius concludes that Hamlet has gone mad with love because, on Polonius's orders, Ophelia stopped speaking with him.
Polonius decides Hamlet really did love Ophelia after all, but does not apologize to his daughter.